Answer: x = 21
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Explanation:
The exponent rules are
- a^b * a^c = a^(b+c) .... lets call this rule 1
- (a^b)/(a^c) = a^(b-c) .... lets call this rule 2
- (a^b)^c = a^(b*c) ......... lets call this rule 3
The expression on the right hand side simplifies to c^(-1). We add the exponents to get this. So we're using rule 1 mentioned above.
We'll keep this in mind for later.
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On the left hand side (c^5)^4 becomes c^(20) because we multiply the exponents (rule 3)
Then (c^20)/(c^x) becomes c^(20-x). We subtract exponents here (rule 2).
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After using those exponent rules, the original equation turns into
c^(20-x) = c^(-1)
The bases are both c, so the exponents must be equal
20-x = -1
-x = -1-20
-x = -21
x = 21
